Home sales are at their highest for nearly four years, according to the Royal Institution of Chartered Surveyors (RICS).
The average number of properties sold by each chartered surveyor was 18.7 in the three months to September - the highest figure since November 2009, though still historically low.
RICS members also reported price rises, with 54% more respondents saying they had experienced rises rather than falls. RICS pointed out that "significantly, this growth was seen right across the UK".
It said prices rose in every part of the country in September - apart from in the North East where prices fell for the second month in a row.
The month also saw a net balance of 49% more surveyors reporting rises in new buyer enquiries.
RICS members expect the property market to get even busier over the next few months with 56% more respondents anticipating the number of sales to increase, while 48% more predict prices to continue to rise.
Peter Bolton King, RICS global residential director, said: "It's encouraging that the market is starting to improve in all parts of the country with more buyers looking to make a move and more sales going through.
"Even so, it's a big concern that the supply of property coming to the market is lagging so far behind demand. This imbalance is likely to result in further upward pressure in prices over the coming months, particularly in the nation's hotspots."